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- W4385327926 abstract "Diffusive limit of the Vlasov-Poisson-Boltzmann system with cutoff soft potentials $-3<gamma<0$ in the perturbative framework around global Maxwellian still remains open. By introducing a new weighted $H_{x,v}^2$-$W_{x,v}^{2, infty}$ approach with time decay, we solve this problem for the full range of cutoff potentials $-3<gammaleq 1$. The core of this approach lies in the interplay between the velocity weighted $H_{x,v}^2$ energy estimate with time decay and the time-velocity weighted $W_{x,v}^{2,infty}$ estimate with time decay for the Vlasov-Poisson-Boltzmann system, which leads to the uniform estimate with respect to the Knudsen number $varepsilonin (0,1]$ globally in time. As a result, global strong solution is constructed and incompressible Navier-Stokes-Fourier-Poisson limit is rigorously justified for both hard and soft potentials. Meanwhile, this uniform estimate with respect to $varepsilonin (0,1]$ also yields optimal $L^2$ time decay rate and $L^infty$ time decay rate for the Vlasov-Poisson-Boltzmann system and its incompressible Navier-Stokes-Fourier-Poisson limit. This newly introduced weighted $H_{x,v}^2$-$W_{x,v}^{2, infty}$ approach with time decay is flexible and robust, as it can deal with both optimal time decay problems and hydrodynamic limit problems in a unified framework for the Boltzmann equation as well as the Vlasov-Poisson-Boltzmann system for the full range of cutoff potentials. It is also expected to shed some light on the more challenging hydrodynamic limit of the Landau equation and the Vlasov-Poisson-Landau system." @default.
- W4385327926 created "2023-07-28" @default.
- W4385327926 creator A5044967169 @default.
- W4385327926 creator A5046487139 @default.
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- W4385327926 date "2023-07-26" @default.
- W4385327926 modified "2023-10-18" @default.
- W4385327926 title "Diffusive Limit of the Vlasov-Poisson-Boltzmann System for the Full Range of Cutoff Potentials" @default.
- W4385327926 doi "https://doi.org/10.48550/arxiv.2307.14088" @default.
- W4385327926 hasPublicationYear "2023" @default.
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